1. Field of the Invention
The invention relates to a Fuzzy backward reasoning device useful for application fields requiring reasoning of a cause of a feature quantity such as for example target classification in air traffic control, diagnoses in medical services and fault diagnoses in plants, etc.
2. Description of the Prior Art
Referring to FIG. 10, a prior art Fuzzy backward reasoning device is illustrated in a block diagram. The device is disclosed for example in "Method of Solution to Fuzzy Inverse Problem" Tsukamoto and Tashiro, Papers in the 3rd System Symposium supported by the Society of Instrument and Control Engineers, Vol. 15, No. 1, p.p. 21 to 25, 1979. As shown in the same figure, designated at 51 is batch reasoning means for receiving all of feature quantities [b.sub.j ] and causality relations [ .sub.j ] for Fuzzy backward reasoning and outputting reasoned results [a.sub.i ], 3 is causality relation storage means for outputting the causality relations [ .sub.j ] previously stored in the batch reasoning means, 5 is a Fuzzy backward reasoning device composed of the batch reasoning means 51 and the causality relation storage means.
The foregoing feature quantities [b.sub.j ], causality relations [ .sub.j ], and reasoned results [a.sub.i ] are Fuzzy vectors, respectively, and the feature quantities [b.sub.j ] express observed failure phenomena and the reasoned results [a.sub.i ] express reasoned failure causes and the like.
Referring to FIG. 11, there is illustrated the principle of the Fuzzy backward reasoning. In the figure, designated at 52 are causality relations corresponding to [ .sub.j ] described above. The logically true causality relation 52 has m limitable true causes a.sub.1, a.sub.2 . . . , a.sub.m, and induces n observable feature quantities b.sub.1, b.sub.2, . . . , b.sub.n. a.sub.i, b.sub.j take values from 0 to 1 and indicate the degree of occurrence of those feature quantities. These quantities are expressed by row vectors EQU =[a.sub.1, a.sub.2 . . . a.sub.m ] (1) EQU =[b.sub.1, b.sub.2 . . . b.sub.n ] (2).
The causality relation 52 as a rule is represented by a m x n matrix =[r.sub.ij ] with elements r.sub.ij taking a value of from 0 to 1, each element indicating a degree where the feature quantity b.sub.j is caused by the cause a.sub.i. If vectors of each column are designated by .sub.j, then they denote a causality relation that causes the feature quantities b.sub.j. Herein, the matrix is expressed by ##EQU1##
The relationship among , , and , illustrated in FIG. 11 satisfies EQU .smallcircle. = (4).
Herein, the symbol .smallcircle. indicates max-min composition. That is, for each element ##EQU2## Herein, denotes max operation and min operation. The causality relation is given as a knowledge and the feature quantity is observable. Hereby, the cause that causes such a feature quantity can be reasoned. The reasoning is given by the Fuzzy backward reasoning. A result of the reasoning gives EQU =[a.sub.1, a.sub.2 . . . a.sub.m ] (6).
More specifically, the Fuzzy backward reasoning device 5 receives the feature quantities of from b.sub.1 to b.sub.n from the outside, and reads out the causality relation 52 of from .sup.1 to .sup.n through the causality relation storage means 3. It further estimates the reasoned values a.sub.1 to a.sub.m corresponding to the causes a.sub.1 to a.sub.m, using the batch reasoning means 51, and outputs those reasoned values.
Referring now to FIG. 12, a flow chart indicative of operation of calculating the reasoned values a.sub.i by the prior art Fuzzy backward reasoning device 5 is illustrated. The operation will be described exemplarily. It is assumed that the causality relation from the causality relation memory means 3 and the observed feature quantities are inputted into the batch reasoning means 51 from the outside, as follows for example. ##EQU3##
First in step T1, the number p of the solutions (the reasoned values a.sub.i) is initialized. Then, in step T2, a matrix is calculated according to the following equation. ##EQU4## Herein, [b.sub.j, 1.0] indicates a closed interval from b.sub.j to 1.0 and .phi. means a null set or no solution. Likewise, in step T3 a matrix is calculated according to the following relation. ##EQU5##
In the example expressed by the equations (7), (8), , are given as follows. ##EQU6##
In step T4, the number L of combinations of non-.phi. elements of respective columns of is calculated. With expressed by (11), EQU L=3.times.3.times.1=9 (13).
In step T5, if L is zero, then there is no solution, and the operation advances to step T12 to output "no solution". If L is not zero, then L solutions must be taken into consideration. In step T6, one element of each column of which is not .phi. is taken out, and remaining elements are taken out from , to form a matrix .sup.k. In the present example, includes 9 combinations, one of which is as follows, for example. ##EQU7##
In step T7, a product set of the ith row of .sup.k is taken out to yield the ith element of . of the expression (14) gives EQU =[(0.9, 1.0)0.0 0.0] (15).
In step T8, if there is any .phi. element among those elements of , i.e., if there is not yielded any product set in any row of .sup.k, then in this case is not taken as a reasoned result. In step T9, the number of reasoned results is counted. In step T10, a resulting reasoned result, e.g., of the expression (15) is outputted. Finally, after L combinations of are estimated, in step T11 if P=0, i.e., if no reasoned result is yielded finally, then the operation jumps to step T12 in which it decides and outputs "no solution".
The prior art Fuzzy backward reasoning device arranged as described above however has a difficulty that the reasoning can be initiated only after all feature quantities b.sub.1 to b.sub.n have been observed. It further has another difficulty that a processor with a higher computational capability is required because the associated computation must be done at a spot.
Alternatively, there is known a prior art target recognition device disclosed as a typical in, for example, Bir Bhanu: Automatic Target Recognition: State of the Art Survey, IEEE Transactions on Aerospace and Electronics, Vol. AES-22, No. 4, p.p. 364-379 (1986), as illustrated in FIG. 13. As illustrated in the figure, designated at 101 is a target to be recognized, 151 is an image sensor for observing the target 101 and outputting image information, 152 is a preprocessor for receiving the image information from the image sensor 151, 153 is a target detector for receiving an output from the preprocessor, 154 is a segmentation for receiving an output from the target detector 153, 155 is a recognizer for receiving an output from the segmentation 154, 156 is a prior typical target recognition device composed of the image sensor 151, preprocessor 152, target detector 153, segmentation 154, and recognizer 155, and 7 is a behavior deciding device for receiving an output from the target recognition device 156.
The target recognition device 156 shown in FIG. 13 is to recognize the target 101 as an image, and is operable as follows. First, the image sensor 151 observes the target 101 as an image. For the image sensor 151, there are sometimes available an infrared sensor and a millimeter wave radar. The preprocessor 152 is to receive and previously process an image, the output from the image sensor 151, and output a processed result. This preprocessing includes suppression of involved noise and clutter and emphasis of the contour of an image, for example. The target detector 153 is to receive the image data processed previously as such, and detect from that data a region where there is existent one which might be considered to be a target, and output it. The segmentation 154 performs image processing highly accurately for the detected region, and extracts and outputs a target from the background extremely accurately. The recognizer 155 collates the target image so extracted with images stored in a data base and outputs the name of the kind of a so-coincident target. This is an output from the prior typical target recognition device 156. The output is fed to the behavior deciding device 7 as a guide to decide a behavior to the target.
Such prior art target recognition devices recognize a target based upon a single kind of information (image information, for example, if an image sensor is used.) available from a sensor with use of a Neuman type computer as described above. Those devices however suffer from a difficulty that there can not be obtained any information concerning a target provided no image information is outputted from the image sensor 151 because such a target is located at a long distance and hence is difficult to be observed as having any shape or because a target is existent in clouds and/or in smoke. Furthermore, those devices have another difficulty that it is unclear to what degree information for recognition of a target from the sensor is reliable.